On the use of Radial Point Interpolation Method (RPIM) in a high order continuation for the resolution of the geometrically nonlinear elasticity problems

Askour, Omar; Mesmoudi, Said; Braikat, Bouazza

doi:10.1016/j.enganabound.2019.09.015

Cited by 23 publications

(16 citation statements)

References 53 publications

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“…The parameters c, q, and l can be selected from the numerical tests of each function to stabilize the solution or by using algorithms designed for their determination. In the present work, the selected values of these parameters are chosen from numerical tests as in [29]. The term p j (X ) in (3) is formulated using Pascal's triangle, and a complete basis is usually preferred with m = 3, m = 6, or m = 10 for the linear, the quadratic or the cubic basis function, respectively.…”

Section: Description Of Radial Point Interpolation Methodsmentioning

confidence: 99%

“…The term p j (X ) in (3) is formulated using Pascal's triangle, and a complete basis is usually preferred with m = 3, m = 6, or m = 10 for the linear, the quadratic or the cubic basis function, respectively. The details of the RPIM shape function's construction from (3) are given in [29].…”

Section: Description Of Radial Point Interpolation Methodsmentioning

confidence: 99%

“…In the second method, the RPIM approximation of the new principal unknown ∆T is used. Therefore, by using the shape functions defined in [29], this unknown is approximated at a node of coordinate X as follows:…”

Section: High-order Continuation With Homotopy Transformationmentioning

confidence: 99%

“…Here, n max is the maximal number of time steps at each continuation step. The parameters and the types of RBFs used in this proposed approach are listed in [29]. Computation is carried out in the time interval [0, 100s] for different time steps so that the influence of each step on the continuation step can be tested.…”

Section: D Heat Conduction Over a Square Platementioning

confidence: 99%

“…In this work, we propose the investigation of unsteady nonlinear heat conduction by using the RPIM in HOC coupled with homotopy transformation for the first time. This approach consists in coupling a temporal implicit Euler scheme and homotopy transformation with the HOC developed in [29]. To demonstrate the efficiency and accuracy of this algorithm, two examples are discussed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Mesmoudi¹,

Askour²,

Braikat³

2020

Comptes Rendus. Mécanique

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Section: Description Of Radial Point Interpolation Methodsmentioning

confidence: 99%

Section: Description Of Radial Point Interpolation Methodsmentioning

confidence: 99%

Section: High-order Continuation With Homotopy Transformationmentioning

confidence: 99%

Section: D Heat Conduction Over a Square Platementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Mesmoudi¹,

Askour²,

Braikat³

2020

Comptes Rendus. Mécanique

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Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Mesmoudi

Askour

Rammane

et al. 2022

Numerical Meth Engineering

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The main objective of the present work is to couple the spectral Chebyshev differential quadrature method (SCDQM) to the high order continuation method (HOCM) which was proposed in previous works with several discretization techniques. This new approach (SCDQM-HOCM) is proposed to analyze the nonlinear bending and buckling analysis of functionally graded sandwich beams.The originality of this work consists also to use a beam model which taken into account the nonlinear term neglected in several works of the literature. This term makes it possible to have the buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. A strong form of nonlinear equations is established based on the first order shear deformation theory of beams with the von-Kármán kinematic hypothesis. Regarding functionally graded materials (FGM), two typical types are investigated: sandwich beam with FGM faces and ceramic core (Type-A), and sandwich beam with FGM core and uniform faces (Type-B). The accuracy and efficiency of the SCDQM-HOCM compared with finite element method coupled with high order continuation method (FEM-HOCM) are illustrated on numerical examples of the FGM beams and then the FG sandwich beams. Furthermore, a parametric study is led to carry out the influence of different skin-core-skin thickness ratios, span-to-height ratio, and volume fraction on the bending and buckling behavior of FG sandwich beams subjected to different loadings and various boundary conditions. K E Y W O R D Sfirst order shear deformation theory, geometrically nonlinear Timoshenko FGM beam, high order continuation method, sandwich Timoshenko FGM beam, spectral Chebyshev differential quadrature method

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Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

Askour,

Rammane,

Mesmoudi

et al. 2024

Numerical Meth Engineering

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SummaryThis study aims to analyze the buckling and post‐buckling behaviors of multilayer nanocomposite beams reinforced with graphene oxide powders (GOPs) at low concentrations. The GOPs are randomly oriented and evenly distributed throughout the composite layers, with their weight fraction varying in the thickness direction. The Halpin‐Tsai model is employed to estimate each layer's effective material properties. The nonlinear governing equations for the FG‐GOPRC beam are derived based on the first‐order shear deformation beam theory, and a nonlinear algebraic system is formulated using the principle of potential energy. In this research, a comprehensive parametric analysis is conducted to examine the influence of various factors on the buckling and post‐buckling behaviors of the composite beams. These factors include the distribution pattern and weight fraction of graphene platelets (GPLs) nanofillers, as well as the geometry, size, slenderness ratio, and boundary conditions of the beams. Through the analysis, the study highlights the significant strengthening effect of these factors on the buckling and post‐buckling performance of the composite beams. The findings from this investigation contribute to a deeper understanding of the behavior of multilayer nanocomposite beams reinforced with GOPs. This knowledge can be valuable in designing and optimizing of composite structures for enhanced buckling resistance and post‐buckling performance.

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On the use of Radial Point Interpolation Method (RPIM) in a high order continuation for the resolution of the geometrically nonlinear elasticity problems

Cited by 23 publications

References 53 publications

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

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